Television Chances

Probability Level 1

Let $X$ be the number of televisions for a household chosen randomly. It is given that

$\begin{aligned} P(X=1) & = 0.18, \\ P(X=2) & = 0.36, \\ P(X=3) & = 0.34, \\ P(X=4) & = 0.08, \\ P(X=5) & = 0.04. \end{aligned}$

If $P(X < 5) = a$ , what is the value of $100a$ ?

5 solutions

Rindell Mabunga
Dec 30, 2013

We know that $P(success) = 1 - P(failure)$ .

Therefore $P(X < 5) = 1 - P(X = 5)$ .

If we sum up all the probabilities given, the result is $1$ so this equation holds.

$P(X < 5) = 1 - P(X = 5)$

$a = 1 - 0.04$

$a = 0.96$

$100a =$ 96

Sọc Chính
Dec 29, 2013

Because P(X<5)= P(X=1) + P(X=2) + P(X=3) + P(X=4) =a Thus, a= 0.18 + 0.36 + 0.34 + 0.08= 0.96 Then 100a=96

That's the solution! But I would like to say that this question asserts that no house has zero televisions!

Sam Dreilinger - 7 years, 5 months ago

Abe Vallerian
Dec 29, 2013

$P(X<5) = 1-P(X=5)= 1-0.04 = 0.96$ Hence, $100a = 96$ .

Hùng Minh
Dec 29, 2013

P(X=5)=0.04 <=> P(X<5) = 1 - P(X=5) = 1 -0.04 = 0.96 = a <=> 100a = 96

Abc Def
Dec 29, 2013

P(X<5) = P(X=1) + P(X=2) + P(X=3) + P(X=4) Hence P(X<5) is 0.96 and 100*0.96 = 96 which is the answer.